Finite Group Databasebeta

Q64×D227 #44402037

order29056
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D227

Splittings

FittingQ64×C227 ⋊ C2
SylowC227 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D227
commutator, cosocleC16×C227C23
FrattiniC16C22×D227
FittingQ64×C227C2
socleC2×C227C2×D16
prime radicalC2×D227D16
hypercenterQ64D227
hypocenterC227C2×Q64
LCSG ▷ C16×C227 ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

2185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6813);